Abstract

We describe the results of an extremely deep, 0.28 deg2 survey for
z=3.1 Lyα emission-line galaxies in the Extended Chandra
Deep Field South. By using a narrow-band 5000 Å filter and complementary
broadband photometry from the MUSYC survey, we identify a statistically
complete sample of 162 galaxies with monochromatic fluxes brighter than
1.5×10−17 ergs cm−2 s−1 and observers frame equivalent
widths greater than 80 Å. We show that the equivalent width
distribution of these objects follows an exponential with a rest-frame scale
length of w0=76+11−8 Å. In addition, we show that in the emission
line, the luminosity function of Lyα galaxies has a faint-end power-law
slope of α=−1.49+0.45−0.34, a bright-end cutoff of
logL∗=42.64+0.26−0.15, and a space density above our detection
thresholds of 1.46±0.12×10−3h703 galaxies Mpc−3.
Finally, by comparing the emission-line and continuum properties of the
LAEs, we show that the star-formation rates derived from Lyα
are ∼3 times lower than those inferred from the rest-frame UV continuum.
We use this offset to deduce the existence of a small amount of internal
extinction within the host galaxies. This extinction, coupled with the lack
of extremely-high equivalent width emitters, argues that these galaxies are not
primordial Pop III objects, though they are young and relatively chemically
unevolved.

The past decade has seen an explosion in our ability to detect and study
z>3 galaxies and probe the history of star formation in the universe
(e.g., Madau et al., 1996). This has been mostly due to the development of the
Lyman-break technique, whereby high redshift galaxies are identified via a
flux discontinuity caused by Lyman-limit absorption (see Steidel et al., 1996a, b). By taking deep broadband images, and searching for U,
B, and V-band dropouts, astronomers have been able to explore large-scale
structure and determine the properties of bright (L>0.3L∗) galaxies
between z∼3 and z∼5(Giavalisco, 2002).

The stunning success of the Lyman-break technique stands in contrast
to the initial results of Lyα emission-line observations. The failure
of the first generation of these surveys (e.g., De Propis et al., 1993; Thompson, Djorgovski, & Trauger, 1995)
was attributed to internal extinction in the target galaxies (Meier & Terlevich, 1981).
Since Lyα photons are resonantly scattered by interstellar hydrogen,
even a small amount of dust can reduce the emergent emission-line flux
by several orders of magnitude.

Fortunately, Lyα surveys
have recently undergone a resurgence. Starting with the Keck observations of
Cowie & Hu (1998) and Hu, Cowie, & McMahon (1998), narrow-band searches for Lyα emission
have been successfully conducted at a number of redshifts, including
z∼2.4(Stiavelli et al., 2001), z∼3.1(Ciardullo et al., 2002; Hayashino et al., 2004; Venemans et al., 2005; Gawiser et al., 2006a), z∼3.7(Fujita et al., 2003), z∼4.5(Rhoads et al., 2000),
z∼4.9(Ouchi et al., 2003), z∼5.7(Rhoads et al., 2003; Ajiki et al., 2003; Tapken et al., 2006),
and z∼6.5(Kodaira et al., 2003; Taniguchi et al., 2005). The discovery of these
high-redshift Lyα emitters (LAEs) has opened up a new frontier
in astronomy. At z>4, LAEs are as easy to detect than Lyman-break
galaxies (LBG), and, by z>6, they are the only galaxies observable from
the ground. By selecting galaxies via their Lyα emission, it is
therefore possible to probe much further down the galaxy continuum
luminosity function than with the Lyman-break technique, and perhaps
identify the most dust-free objects in the universe. In addition, by
using Lyα emitters as tracers of large-scale structure
(Steidel et al., 2000; Shimasaku et al., 2004), it is possible to efficiently probe
the expansion history of the universe with a minimum of cosmological
assumptions (e.g., Blake & Glazebrook, 2003; Seo & Eisenstein, 2003; Koehler et al., 2007).

Here, we describe the results of a deep survey for Lyα emission-line
galaxies in a 0.28 deg2 region centered on the Extended Chandra Deep
Field South (ECDF-S). This region has an extraordinary amount of
complementary data, including high-resolution optical images from the
Hubble Space Telescope via the Great Observatories Origins Deep
Survey (GOODS; Giavalisco et al., 2004) and the Galaxy Evolution from Morphology
and SEDs program (GEMS; Rix et al., 2004), deep groundbased UBVRIzJHK
photometry from the Multiwavelength Survey by Yale-Chile
(MUSYC; Gawiser et al., 2006b), mid- and far-IR observations from Spitzer,
GOODS and MUSYC, and deep X-ray data from Chandra(Giacconi et al., 2002; Alexander et al., 2003; Lehmer et al., 2005). In Section 2, we describe our observations, which
include over 28 hours worth of exposures through a narrow-band filter on
the CTIO 4-m telescope. We also review the techniques used to detect the
emission-line galaxies, and discuss the difficulties associated with
analyzing samples of LAEs discovered via fast-beam instruments. In
Section 3, we describe the continuum properties of our Lyα emitters,
including their rest-frame m1050−m1570 colors, and compare their
space density to that of Lyman-break galaxies. In Section 4, we examine the
LAE’s equivalent width distribution and show that our sample contains very
few of the extremely-high equivalent width objects found by
Dawson et al. (2004) at z=4.5. In Section 5, we present the Lyα
emission-line luminosity function, and give values for its best-fit
Schechter (1976) parameters and normalization. In Section 6, we translate
these Lyα fluxes into star-formation rates, and consider the properties
of LAEs in the context of the star-formation rate (SFR) history of
the universe. We conclude by discussing the implications our
observations have for surveys aimed at determining cosmic evolution.

For our analysis, we adopt a ΛCDM cosmology with
H0=70 km s−1 Mpc−1 (h70=1), ΩM=0.3, and
ΩΛ=0.7. At z=3.1, this implies a physical scale
of 7.6 kpc per arcsecond.

Narrow-band observations of the ECDF-S were performed with the MOSAIC II
CCD camera on the CTIO Blanco 4-m telescope. These data consisted of a
series of 111 exposures taken over 16 nights through a
50 Å wide full-width-half-maximum (FWHM) λ5000 filter (see
Figure 1). The total exposure time for these images was
28.17 hr; when the effects of dithering to cover for a dead CCD during
some of the observations are included, the net exposure time becomes
∼24 hr. The total area covered in our survey is 998 arcmin2;
after the regions around bright stars are excluded, this area shrinks
993 arcmin2. The overall seeing on the images is 1\farcs0.
A log of our narrow-band exposures appears in Table 1.

The procedures used to reduce the data, identify line emitters, and measure
their brightnesses were identical to those detailed in Ciardullo et al. (2002) and
Feldmeier et al. (2003). After de-biasing, flat-fielding, and aligning the data, our
narrow-band frames were co-added to create a master image that was clipped
of cosmic rays. This frame was then compared to a deep B+V continuum
image provided by the MUSYC survey (Gawiser et al., 2006b) in two different ways.
First, the DAOFIND task within IRAF was run on the summed narrow-band and
continuum image using a series of three convolution kernels, ranging from
one matching the image point-spread-function (PSF), to one ∼3 times
larger. This created a source catalog of all objects in our field. These
targets were then photometrically measured with DAOPHOT’s PHOT routine, and
sources with on-band minus continuum colors less than −1.03 in the AB system
were flagged as possible emission-line sources (see Figure 2). At
the same time, candidate LAEs were also identified by searching for positive
residuals on a “difference” image made by subtracting a scaled version of
the B+V continuum image from the narrow-band frame. In this case, the
DAOFIND algorithm was set to flag all objects brighter than four times the
local standard deviation of the background sky (see Figure 3).
As pointed out by Feldmeier et al. (2003), these two techniques complement each other,
since each detects objects that the other does not. Specifically,
≲10% of galaxies were missed by the color-magnitude method
due to image blending and confusion, but found with the difference method.
Conversely, objects at the frame limit that were lost amidst the increased
noise of the difference frame, could still be identified via their on-band
minus off-band colors.

Finally, because we intentionally biased our DAOFIND parameters to identify
faint sources at the expense of false detections, each emission-line candidate
was visually inspected on the narrow-band, B+V continuum, and difference
frames, as well as two frames made from subsamples of half the on-band
exposures. This last step excluded many false detections at the frame
limit, and left us with a sample of 259 candidate LAEs for analysis.

Once found, the equatorial positions of the candidate emission-line galaxies
were derived with respect to the reference stars of the USNO-A 2.0 astrometric
catalog (Monet et al., 1998). The measured residuals of the plate solution
were ∼0\farcs2, a number slightly less than the 0\farcs25 external
error associated with the catalog. Relative narrow-band magnitudes for
the objects were derived by first measuring the sources with respect to
field stars using an aperture slightly greater than the frame PSF.
Since most of the galaxies detected in this survey are, at best, marginally
resolved on our 1\arcsec images, this procedure was sufficiently
accurate for our purposes. We then obtained standard AB magnitudes by
comparing large aperture photometry of the field stars to similar measurements
of the spectrophotometric standards Feige 56 and Hiltner 600 (Stone, 1977)
taken on three separate nights. The dispersion in the photometric zero point
computed from our standard star measurements was 0.03 mag.

2.1 Derivation of Monochromatic Fluxes

The fast optics of wide-field instruments, such as the MOSAIC camera
at the CTIO 4-m telescope, present an especially difficult challenge
for narrow-band imaging. The transmission of an interference filter depends
critically on the angle at which it is illuminated: light entering at the
normal will constructively/destructively interfere at a different
wavelength than light coming in at an angle (Eather & Reasoner, 1969). As a result, when
placed in a fast converging beam, an interference filter will have its bandpass
broadened and its peak transmission decreased by a substantial amount.
This effect is important, for without precise knowledge of the filter
bandpass, it is impossible to derive accurate monochromatic fluxes or
estimate equivalent widths.

To derive the filter transmission, we began with the throughput information
provided by the CTIO
observatory3.
This curve, which represents the expected transmission of the
[O III] interference filter in the f/3.2 beam of the Blanco telescope, was
computed by combining laboratory measurements of the filter tipped at several
different angles from the incoming beam (for a discussion of this
procedure, see Jacoby et al., 1989). We then shifted this curve 2 Å to the blue, to
compensate for the thermal contraction of the glass at the telescope, and
compared this model bandpass to the measured emission-line wavelengths obtained
from follow-up spectroscopy (Lira et al., 2007). Interestingly, redshift
measurements of 72 galaxies detected in three independent MUSYC fields confirm
the shape of the filter’s transmission curve, but not its central wavelength:
according to the spectroscopy, the mean wavelength of the filter is 10 Å bluer than given by CTIO (Gawiser et al., 2007). Examining the source of this
discrepancy is beyond the scope of this paper. However, the data do confirm
that, when placed in the beam of the CTIO 4-m prime focus MOSAIC camera, the
bandpass of the CTIO [O III] interference filter is nearly Gaussian in shape.
This bandpass is reproduced in the left-hand panel of Figure 4.

This non-square bandpass has important consequences for the analysis of
large samples of emission-line galaxies. The first of these involves
the definition of survey volume. Because the transmission of the filter
declines away from the bandpass center, the volume of space sampled by
our observations is a strong function of line strength. This is illustrated
in the center panel of Figure 4. Objects with bright line
emission can be detected even if their redshifts place Lyα
in the wings of the filter, hence the volume covered for these objects is
realtively large. Conversely, weak Lyα sources must have their line
emission near the center of the bandpass to be observable. As a result, the
“effective” volume for our integrated sample of galaxies is a function of
the galaxy emission-line luminosity function.

A second concern deals with the sample’s flux calibration.
In order to compare the flux of an emission-line
object to that of a spectrophotometric standard star (i.e., a continuum
source) one needs to know both the filter’s integral transmission and its
monochromatic transmission at the wavelength of interest (Jacoby et al., 1987, 1989).
When observing objects at known redshift, the latter requirement is not an
issue. However, when measuring a set of galaxies which can fall anywhere
within a Gaussian-shaped transmission curve, the transformation between an
objects’ (bandpass-dependent) AB magnitude and its monochromatic flux is not
unique. In fact, if we assume that galaxies are (on average) distributed
uniformly in redshift space, then the number of emission-line objects present
at a given transmission, T, is simply proportional to the amount of
wavelength associated with that transmission value. Consequently, the observed
distribution of emission-line fluxes will be related to the true
distribution via a convolution, whose (unity normalized) kernel, G(T), is

G(T)dT={∣∣∣dλdT∣∣∣dT}blue+{∣∣∣dλdT∣∣∣dT}red

(1)

where the first term describes the filter’s response blueward of the
transmission peak and the second term gives the response redward of
the peak. The center panel of Figure 4 displays this kernel
for the filter used in our survey. The curve shows that for roughly half of
the detectable galaxies in our field, the effect of our filter’s non-square
bandpass is minimal. However, for the other ∼50% of galaxies, the
shape of the bandpass is extremely important, and the inferred fluxes for some
objects can be off by over a magnitude.

Any analysis of the ensemble properties of our LAEs must consider the full
effect that the non-square bandpass and the odd-shaped convolution kernal
has on the sample. We do this in Sections 4 and 5. However, one often wants
to quote the monochromatic flux and equivalent width for an individual
Lyα emitter. To do this, we need to adopt an appropriate “mean” value
for the transmission of our filter. The most straightforward way
to define this number is via the filter’s peak transmission. This is
where the survey depth is greatest, and choosing Tmax is
equivalent to assigning each galaxy its “most probable” monochromatic
flux. Unfortunately, by defining the transmission in this way,
we underestimate the flux from all galaxies whose line emission does not
fall exactly on this peak. Alternatively, we can attempt to choose a
transmission which globally minimizes the flux errors of all the
galaxies detected in the survey. This can be done by weighting each
transmission by the number of galaxies one expects to observe at that
wavelength: the greater the transmission, the deeper the survey, and the more
galaxies present in the sample. The difficulty with this “expectation
value” approach is that it requires prior knowledge of the distribution of
emission-line fluxes, which is one of the quantities we are attempting
to measure. That leads us to a third possibility: to approximate the
filter’s expectation value using some “characteristic” transmission, TC,
which is independent of the galaxy luminosity function, but still takes
the filter’s changing transmission into account. The arrow in
Figure 4 identifies the transmission we selected as being
characteristic of the filter; the justification for this value is presented
in Section 5. We emphasize that TC is only a convenient mean that
enables us to quote the likely emission-line strengths of individual
galaxies. When analyzing the global properties of an ensemble of LAEs, the
full non-Gaussian nature of the filter’s convolution kernel must be
taken into account.

Using this transmission and our knowledge of the filter curve, we
converted the galaxies’ AB magnitudes to monochromatic fluxes at
λ=5000 Å via

F5000=3.63×10−2010−mAB/2.5⋅cλ2⋅∫TλdλTC

(2)

where F5000 is given in ergs cm−2 s−1(Jacoby et al., 1987).
Equivalent widths then followed via

EW=F5000fB+V−Δλ

(3)

where fB+V is the objects’ AB flux density in the B+V continuum image,
and Δλ, the FWHM of the narrow-band filter, represents the
contribution of the galaxy’s underlying continuum within the bandpass. Both
these equations are only applicable to objects whose line emission dominates
the continuum within the narrow-band filter’s bandpass. Since we are limiting
our discussion to galaxies with narrow-band minus broad-band AB magnitudes
more negative than −1.03, this approximation is certainly valid. However,
we do note that by using TC instead of Tmax, we are intentionally
overestimating the flux and equivalent width of some galaxies, in order to
minimize the errors in others. So, while the application of TC formally
translates our Δm=−1.03 criterion into a minimum emission-line
equivalent width of 90 Å, galaxies with emission-lines that fall near the
peak of the filter transmission function can have equivalent widths that are
∼12% smaller. This implies that the absolute minimum equivalent
width limit for our sample of LAEs is 80 Å.

2.2 Sample of LAE Candidates

Tables 2 and 3
give the coordinates of each candidate emission-line
galaxy, along with its inferred monochromatic flux and equivalent width.
In total, 259 objects are listed, though many are beyond the limit of
our completeness. To determine this limit, we followed the procedures of
Feldmeier et al. (2003) and added 1,000,000 artificial stars (2000 at a time) to our
narrow-band frame. By re-running our detection algorithms on these modified
frames, we were able to compute the flux level below which the object recovery
fraction dropped below the 90% threshold. This value, which corresponds
to a monochromatic flux of 1.5×10−17 ergs cm−2 s−1
(logF5000=−16.82) is our limiting magnitude for statistical
completeness; 162 galaxies satisfy this criterion.

Before proceeding further with our analysis, we performed one additional check
on our data. To eliminate obvious AGN from our sample, we cross-correlated
our catalog of emission-line objects with the lists of X-ray sources found
in the 1 Msec exposure of the Chandra Deep Field South (Alexander et al., 2003),
and the four 250 ksec exposure of the Extended Chandra Deep Field South
(Lehmer et al., 2005; Virani et al., 2006). Two of our LAE candidates were detected in the X-ray
band. The first, which is our brightest Lyα emitter, has a 0.5 – 8 keV
flux of 3.4×10−15 ergs cm−2 s−1 (i.e., LX∼2.8×1044h70−2 ergs s−1 at z=3.1) and exhibits
C IV emission at 1550 Å (Lira et al., 2007). The other is an interloper:
a z=1.6 AGN detected via its strong C III] line at 1909 Å.
For the remaining 160 objects that were not detected individually in the X-ray
band, we used stacking analyses to constrain their mean X-ray power output
(see Lehmer et al., 2007, for details). We find that the stacked X-ray
signal, which corresponds to a ∼40 ksec effective exposure on an
average LAE, does not yield a 3σ detection in any of three
X-ray bandpasses (0.5–8.0 keV, 0.5–2.0 keV, and
2–8 keV). These results imply a 3σ upper-limit of
∼3.8×1041h−270 ergs s−1 on the mean
0.5–2.0 keV luminosity for our LAEs, which demonstrates that few
of our Lyα sources harbor low-luminosity AGN. Similarly,
if we use the conversion of Ranalli et al. (2003), we can translate this
X-ray non-detection into an upper-limit for a typical LAE’s
star-formation rate. This limit, 85h70−2M⊙ yr−1,
is roughly an order of magnitude greater than the rates inferred from the
objects’ Lyα emission or UV continua (see Section 6).

For the remainder of this paper, we will treat our z=3.1 X-ray source
as AGN and exclude it from the analysis. This leaves us with a sample of
160 objects, which we assume are all star-forming galaxies. We note that,
because all of our objects have equivalent widths greater than
80 Å, they are unlikely to be [O II] emitters. At z∼0.34,
our survey volume is only ∼7300h70−3 Mpc3,
which, through the luminosity functions of Hogg et al. (1998), Gallego et al. (2002), and Teplitz et al. (2003), implies a total population of
between ∼20 and ∼200 [O II] emission-line galaxies above
our completeness limit. Since less than 2% of these objects will have
rest frame equivalent widths greater than ∼60 Å (Hogg et al., 1998),
the number of [O II] interlopers in our sample should be negligible.
This estimate is confirmed by follow-up spectroscopy: of the 52 LAE
candidates observed with sufficient signal-to-noise for a redshift
determination, all are confirmed Lyα emitters
(Gawiser et al., 2006a; Lira et al., 2007).

Figure 5 shows the spatial distribution of the LAEs
above our completeness limit. The sources are obviously clustered,
falling along what appear to be “walls” or “filaments”. The
GOODS region has a below-average number of z=3.1 Lyα emitters,
and there are almost no objects in the northwestern part of the field.
Conversely, the density of LAEs east and northeast of the field center is
quite high. This type of data can be an extremely powerful probe of
cosmological history, but we will defer a discussion of this topic
to a future paper (Gawiser et al., 2007).

To investigate the continuum properties of our Lyα emitters, we
measured the brightness of each LAE on the broadband UBVR images of the
MUSYC survey (Gawiser et al., 2006b). Since the catalog associated with this dataset
has a 5σ detection threshold of U=26.0, B=26.9, V=26.4,
and R=26.4, our knowledge of the LAEs’ positions (obtained from
the narrow-band frames) allows us to perform photometry well past this limit.
Figure 6 displays the B−R color-magnitude diagram for 88 of the LAEs
brighter than RAB=27.25. The diagram, which shows the
galaxies’ rest-frame continua at 1060 and 1570 Å, has several features
of note.

The first involves the color distribution of our objects. According to
the figure, LAEs with R-band magnitudes brighter than R=25 have a
median color of B−R=0.53. This value agrees with the blue colors found
by Venemans et al. (2005) for a sample of Lyα emitters at z=3.13, and
is the value expected for a ∼108 yr old stellar system evolving with
a constant star-formation rate (Fujita et al., 2003; Bruzual & Charlot, 2003). This median color
is also consistent with the results of Gawiser et al. (2006a), who stacked the
broad-band fluxes of 18 spectroscopically confirmed z=3.1 LAEs and
showed that the typical age of these systems is between 0.01<t<2 Gyr.
It does, however, stand in marked contrast to the results of
Stiavelli et al. (2001), who claimed that Lyα emitters at z=2.4 are
very red (B−I∼1.8). The blue colors of our galaxies confirm their
nature as young, star-forming systems. There is no evidence for excessive
reddening in these objects, and if the galaxies do possess an underlying
population of older stars, the component must be quite small.

On the other hand, as the LAE color distribution indicates, Lyα
emitters are not, as a class, homogeneous. At R=25, the MUSYC B−R
colors have a typical photometric uncertainty of σB−R=0.25 mag.
This contrasts with the observed color dispersion for our galaxies, which is
∼0.4 mag for objects with R<25. Thus, there is at least a
∼0.3 mag scatter in the intrinsic colors of these objects. Either there
is some variation in the star-formation history of Lyα emitters, or
dust is having an effect on the emergent colors.

Finally, it is worth emphasizing that our Lyα emitters are substantially
fainter in the continuum than objects found by the Lyman-break technique.
At z∼3, L∗ galaxies have an apparent magnitude of
R∼24.5(Steidel et al., 1999) and ground-based Lyman-break surveys
typically extend only ∼1 mag beyond this value
(see Giavalisco, 2002, for a review). Furthermore, spectroscopic surveys of
LBG candidates rarely target galaxies fainter than R=24. In our
emission-line sample, the median continuum magnitude is R∼26.7, and
many of the galaxies have aperture magnitudes significantly fainter than
R∼28. In general, LAEs do inhabit the same location as LBGs in the
U-V vs. V-R color-color space (see Figure 7), but
their extremely faint continuum sets them apart.

This is also illustrated in Figure 8, which compares the
rest frame 1570 Å luminosity function of our complete sample of
Lyα emitters (those with monochromatic fluxes greater than
1.5×10−17 ergs cm−2 s−1) with the rest-frame
1700 Å luminosity function of z=3.1 Lyman-break galaxies
(Steidel et al., 1999). When plotted in this way, our sample of LAEs appears
incomplete, since for R≳26.5, only the brightest emission-line
sources will make it into our catalog. The plot also implies that at
z=3.1, R<25.5, Lyα emitters are ∼3 times rarer than
comparably bright Lyman-break galaxies. Since this ratio is virtually
identical to that measured by Steidel et al. (2000) within an extremely rich
z=3.09 protocluster, this suggests that the number is not a strong
function of galactic environment. But, most strikingly, our observations
demonstrate the Lyα emitters sample the entire range of the
(UV-continuum) luminosity function. The median UV luminosity of LAEs in our
sample is ≲0.2L∗, and the faintest galaxy in the group is no
brighter than ∼0.02L∗. Just as broadband observations
detect all objects at the bright-end of the continuum luminosity function, but
sample the entire range of emission-line strengths, our narrow-band
survey finds all the brightest emission-line objects, but draws from the
entire range of continuum brightness.

Before examining the emission-line properties of our dataset,
we need to correct for the observational biases and selection
effects that are present in the sample. Since the data were taken
in a fast-beam through a filter with a non-square bandpass, these effects are
substantial. Continuum measurements, of course, are unaffected by the
peculiarities of a narrow-band filter, but the distribution of monochromatic
fluxes can be significantly distorted. Specifically, the observed flux
distribution will be the convolution of the true distribution with the
following two kernels:

The Photometric Error Function: The random errors associated with
our narrow-band photometry vary considerably, ranging from
∼0.02 mag at the bright end, to ∼0.2 mag near the completeness
limit (see Table 4).
These errors will scatter objects from heavily
populated magnitude bins into bins with fewer objects, and flatten the
slope of the luminosity function. Because the change in slope goes as the
square of the measurement uncertainty (Eddington, 1913, 1940), the
effect of this convolution is most important for objects near the survey
limit.

The Filter Transmission Function. As described in Section 2.1, the
narrow-band filter used for this survey has a transmission function that is
nearly Gaussian in shape. This creates an odd-shaped convolution kernel (the
right panel of Figure 4), which systematically decreases the
measured line-emission of objects falling away from the peak of the
transmission curve. Moreover, because the objects’ equivalent widths are
also reduced by this bandpass effect, some fraction of the LAE population will
be lost from our EW >80 Å sample. The result is that the
normalization of this filter transmission kernel is not unity. Instead, it
depends on the intrinsic equivalent width distribution of the galaxies, since
that is the function that defines the fraction of galaxies (at each redshift)
which can still make it into our sample.

These effects are illustrated in the top panel of Figure 9, which
displays a histogram of the rest-frame equivalent widths for our candidate
Lyα galaxies. As the dotted line shows, the data appear to be well
fit by an exponential that has an e-folding length of
wobs=214+19−15 Å. However, because
the bandpass of our narrow-band filter is more Gaussian-shaped than
square, the line-strengths of many of the galaxies have been
systematically underestimated. In fact, the true distribution of equivalent
widths is broader than that measured: when we perform a
maximum-likelihood analysis using a series of exponential laws, convolved
with the filter bandpass and photometric error kernels, we obtain a
most-likely scale length of wobs=311+47−33 Å, or
w0=76+11−8 Å in the rest frame of the sample.

Such a distribution is quite different from that reported by
Malhotra & Rhoads (2002). In their survey of 150 z=4.5 Lyα emitters,
∼60% of the objects had extremely high rest-frame equivalent widths,
i.e., EW0>240 Å. Since stellar population models, such as those
by Charlot & Fall (1993) cannot produce such strong line-emission, Malhotra & Rhoads (2002)
postulated the presence of a top-heavy initial mass function and perhaps
the existence of Population III stars. However in our sample, only 3
out of 160 LAEs (∼2%) have observed rest-frame equivalent widths
greater than this 240 Å limit. Even when we correct for the effects
of our filter’s non-square bandpass, the fraction of strong line-emitters does
not exceed ∼12%. This is less than the ∼20%
value estimated by Dawson et al. (2004) via Keck spectroscopy of a subset
of Malhotra & Rhoads (2002) objects. Thus, at least at z∼3.1, there is no
need to invoke a skewed initial mass function to explain the majority of our
LAEs.

The equivalent width distribution of Figure 9 also differs
dramatically from that found by Shapley et al. (2003) for a sample of
z∼3 Lyman-break galaxies. In their dataset, rest-frame equivalent
widths e-fold with a scale-length of ∼25 Å, rather than the
∼75 Å value derived from our LAE survey. This difference is
not surprising given that the former dataset is selected to be bright
in the continuum, while the latter is chosen to be strong in the
emission-line. Moreover, when Shapley et al. (2003) analyzed the ∼25%
of Lyman-break galaxies with rest-frame equivalent widths greater than
20 Å, they found a correlation between line strength and continuum
(R-band) magnitude, in the sense that fainter galaxies had higher
equivalent widths. We see that same trend in our data, but it is
largely the result of a selection effect. (Faint galaxies with low
equivalent widths fall below our monochromatic flux limit.) A comparison
of emission-line flux with equivalent width for our statistically complete
sample shows no such correlation.

The lower two panels of Figure 9 demonstrate this another way.
In the diagram, our sample of LAEs is divided in half, with the middle panel
showing the equivalent width distribution for objects with monochromatic
Lyα luminosities greater 2×1042h70−2 ergs s−1,
and the bottom panel displaying the same distribution for less luminous
objects. As the figure illustrates, the distribution of equivalent widths
is relatively insensitive to the absolute brightness of the galaxy. To
first order this is expected, since both the UV continuum and the Lyα
emission-line flux are driven by star formation. However, one could imagine
a scenario wherein the amount, composition, and/or distribution of dust within
the brighter (presumably more-metal rich) Lyα emitters differs from
that within their lower-luminosity counterparts. Since the effect of this
dust on resonantly-scattered Lyα photons is likely to be different
from that on continuum photons, this change in extinction can theoretically
produce a systematic shift in the distribution of Lyα equivalent
widths. There is no evidence for such a shift in our data; this constancy
argues against the importance of dust in these objects.

Figure 10 shows the distribution of monochromatic fluxes for our
sample of emission-line galaxies. The function looks much like a power
law, with a faint-end slope of α∼−1.5 that steepens as one moves
to brighter luminosities. However, to quantify this behavior, we once again
have to correct the observed flux distribution for the distortions caused by
photometric errors and the non-square bandpass of the filter. In addition, we
must also consider the censoring effect our equivalent width cutoff has on the
data: some line emitters whose redshifts are not at the peak of the filter
transmission function will fall out of our sample completely.

To deal with these effects, we fit the observed distribution of Lyα
emission-line fluxes to a Schechter (1976) function via the method
of maximum likelihood (e.g., Hanes & Whittaker, 1987; Ciardullo et al., 1989). We applied our two
convolution kernels (including the equivalent width censorship) to a series
of functions of the form

ϕ(L)d(L/L∗)∝(L/L∗)αe−L/L∗d(L/L∗)

(4)

treated each curve as a probability distribution (i.e., with a unity
normalization), and computed the likelihood that the observed sample of
Lyα fluxes is drawn from the resultant distribution. The results for
the three parameters of this fit, α, logL∗, and N, the integral
of the Schechter function down to our limiting flux (in units of
galaxies Mpc−3), are shown in Figure 11;
Table 5 lists the best-fitting parameters, along with their
marginalized most-likely values and uncertainties. For completeness,
Table 5 also gives the value of ϕ∗ which is inferred
from our most likely solution. As expected, the plots
illustrate the familiar degeneracy between L∗ and α: our best-fit
solution has α∼−1.5, but if L∗ is forced to brighter
luminosities, α decreases. The contours also demonstrate an asymmetry
in the solutions, whereby extremely bright values of L∗ are included within
the 3σ contours of probability, but faint values of the same
quantity are not.

But perhaps the most interesting feature of the analysis concerns the effective
volume of our survey. As in Section 2.1, the amount of space sampled by the
observations depends critically on each galaxy’s Lyα luminosity and
equivalent width. Bright line-emitters with large equivalent widths
can be identified well onto the wings of the filter, hence the survey
volume associated with these objects is relatively large. Conversely,
weak line-emitters, and objects with small equivalent widths can only
be detected if they lie at the peak of the filter transmission curve.
Thus, the survey volume for these objects is quite small. The effective
volume for our observations is therefore a weighted average, which
depends on the intrinsic properties of entire LAE sample.

This average can be computed from the data displayed in Figure 11.
According to the figure, the space density of galaxies with emission-line
brighter than 1.5×10−17 ergs cm−2 s−1 (i.e., 1.3×1042h70−2 ergs s−1) is extremely well-defined,
1.46±0.12×10−3h703 galaxies Mpc−3. Since this
measurement comes from the detection of 160 galaxies brighter than the
completeness limit, the data imply an effective survey volume of
∼1.1×105h70−3 Mpc3. This is not
the volume one would infer from the interference filter’s full-width
at half-maximum: it is 25% smaller, or roughly the full-width of
the filter at two-thirds maximum.

This difference is illustrated in Figure 10. The points
show the space density of Lyα galaxies one would derive simply
by using the filter’s FWHM to define the survey volume; the solid line
gives the Schechter (1976) function which best fits the data. The
offset between the solid line and the dashed line, which represents the
function after the application of the two convolution kernels, confirms the
need for careful analysis when working with narrow-band data taken through a
non-square bandpass.

The results of our maximum-likelihood calculation also suggest a simple
definition for the effective transmission for our filter. As described in
Section 2.1, a “characteristic” transmission is needed to convert the
(bandpass-dependent) AB magnitude of an individual galaxy to monochromatic
Lyα flux. Rather than use the maximum transmission (which would
underestimate the flux of all galaxies not at the filter peak), or adopt some
complicated scheme which involves iterating on the luminosity function, one
can simply choose the filter’s mean transmission within some limited
wavelength range. Based on the results above, the filter’s full-width at
two-thirds maximum seems an appropriate limit. This transmission, which is
indicated by the arrow in Figure 4, is the value used to derive
the fluxes and equivalent widths of Tables 2 and
3. If were to use to filter’s peak transmission instead of
this characteristic value, the tabulated emission-line fluxes and equivalent
widths would all be ∼12% smaller.

The error bars quoted above for the space density of Lyα emitters
represent only the statistical uncertainty of the fits. They do not
include the possible effects of large-scale structure within our survey
volume. Specifically, if the linear bias factor for LAEs is two
(see Gawiser et al., 2007, for an analysis of the objects’ clustering) then
the expected fluctuation in the density of Lyα emitters measured within
a ∼105h70−3 Mpc3 volume of space is ∼30%. This
value should be combined in quadrature with our formal statistical
uncertainty.

Since Lyα galaxies have been observed at a number of redshifts,
it is tempting to use our data to examine the evolution of the LAE
luminosity function. Unfortunately, the samples obtained to date are not
yet robust enough for this purpose. An example of the problem is shown in
Figure 12, which compares our cumulative luminosity function
(and our Schechter fit for α=−1.5) to two measures of Lyα
galaxies at z=5.7. As the figure illustrates, there are large differences
between the measurements. If the Malhotra & Rhoads (2004) luminosity function is
correct, then LAEs at z=3.1 are a factor of ∼2.5 brighter and/or
more numerous than their z=5.7 counterparts. However, if the z=5.7
LAE luminosity function of Shimasaku et al. (2006) is correct, then evolution
is occurring in the opposite direction, i.e., the star-formation rate density
is declining with time. Without better data, it is difficult to derive any
conclusions about the evolution of these objects.

Figure 12 also plots our data against the predictions of a
hierarchical model of galaxy formation (Le Delliou et al., 2005, 2006).
As this comparison demonstrates, our luminosity function for z=3.1 LAEs
lies slightly below that generated by theory. This is not surprising:
one of the key parameters of the model, the escape fraction of
Lyα photons, was set using previous estimates of the density of
z∼3 LAEs. Unfortunately, these measurements were based on extremely
small samples of objects, specifically, nine z=3.1 emitters from
Kudritzki et al. (2000) and ten z=3.4 LAEs from Cowie & Hu (1998). Since these surveys
inferred a larger space density of Lyα emitters than measured in this
paper, a mismatch between our data and the Le Delliou et al. (2006) models is
neither unexpected nor significant.

Perhaps the most interesting result of our survey comes from a comparison
of the galaxies’ Lyα emission with their R-band magnitudes.
Both quantities measure star formation rate: Lyα via the combination of
Case B recombination theory and the Hα vs. star formation relation

(Kennicutt, 1998). If both of these calibrations hold for our sample of
Lyα emitters, then a plot of the two SFR indicators should scatter
about a one-to-one relation.

Figure 13 displays this plot. In the figure, galaxies with
Lyα star-formation rates less than ∼1.15M⊙ yr−1 are
excluded by our 1.5×10−17 ergs cm−2 s−1 monochromatic
flux limit, while objects with large UV star-formation rates, but weak
Lyα are eliminated by our equivalent width criterion. The latter
is not a hard limit, since LAE colors range from 0≲(B+V)−R≲2.5, and it is the B+V continuum that is used to define
equivalent width. Nevertheless, if we adopt 1.4 as the upper limit on
the median color of an Lyα emitting galaxy (i.e., 1σ above
the median (B+V)−R∼0.65 color of the population), we obtain the
dotted line shown in the figure.

Despite these selection effects, the Lyα and UV continuum star-formation
rates do seem to be correlated. However, there is an offset: the rates
inferred from the UV are, on average, about three times higher than
those derived from Lyα. While the Lyα SFR measurements are
generally less than 10h70−2M⊙ yr−1, the rest-frame
UV values extend up to ∼50h70−2M⊙ yr−1.
This discrepancy has previously been seen in a sample of 20 LAEs at
z=5.7(Ajiki et al., 2003), and has two possible explanations.

The most likely cause of the offset is the galaxies’ internal
extinction. By studying local starburst galaxies, Calzetti (2001) has shown
that a system’s ionized gas is typically attenuated more than its stars.
In other words, while optical and IR emission-line ratios can usually be
reproduced with a simple screen model, the shape of the UV continuum
requires that the dust and stars be intermingled. For a self-consistent
solution, Calzetti (2001) suggests

E(B−V)stars=0.44E(B−V)gas

(7)

If we apply the Calzetti (2001) law to our sample of z=3.1 Lyα
emitters, then for the UV and Lyα star-formation rates to be equal,
the extinction within our LAEs must be as shown in Figure 14.
According to the figure, in most cases it only requires a small amount of dust
(E(B−V)stars<0.05) to bring the two indicators into
agreement. Figure 14 also suggests that internal
extinction becomes more important in the brighter galaxies. This is
consistent with observations of local starburst systems (e.g., Meurer et al., 1995),
and is expected if the mass-metallicity relation seen in the local universe
carries over to dust content.

Alternatively, the discrepancy between the Lyα and UV continuum
star-formation rates may simply be due to uncertainties in their
estimators. Models which translate UV luminosity into star formation
rate have almost a factor of two scatter and rely on a number of
parameters, including the initial mass function and the timescale for
star formation. The latter is particularly problematic. Lyα
photons are produced almost exclusively by extremely young (<30 Myr),
massive (>10M⊙) stars which ionize their surroundings.
It therefore registers the instantaneous star-formation
occurring in the galaxy. Conversely, continuum UV emission (at 1570 Å)
can be produced by populations as old as ∼1 Gyr; thus, it is a
time-averaged quantity. If the star-formation rate in our Lyα emitters
has declined over time, then it is possible for UV measurements to
systematically overestimate the present day star formation
(Glazebrook et al., 1999).

If we assume that Lyα emission is an accurate measure of
star-formation, then it is possible to integrate the Schechter function
to estimate the total contribution of LAEs to the star-formation rate
density of the z=3.1 universe. We note that this procedure does
carry some uncertainty. If we just consider galaxies brighter than
our completeness limit (1.5×10−17 ergs cm−2 s−1
or LLyα>1.3×1042h70−2 ergs s−1)
then the star-formation rate density associated with LAEs is
∼3.6×10−3h70M⊙ yr−1 Mpc−3, or
1.2×10−2h70M⊙ yr−1 Mpc−3 if the internal
extinction in these objects is E(B−V)stars∼0.05. However,
to compute the total star-formation rate density, we need to extrapolate
the LAE luminosity function to fainter magnitudes, and even 160 objects
is not sufficient to define α to better than ∼25%.
Consequently, our data admit a range of solutions.

This is illustrated in Figure 15, which displays SFR
likelihoods derived from the probabilities illustrated in
Figure 11. As the figure shows, the most likely value
for the LAE star-formation rate density of the z=3.1 universe
(uncorrected for internal extinction) is
6.5×10−3h70M⊙ yr−1 Mpc−3, while
the median value of this quantity (defined as the point
with equal amounts of probability above and below) is 8.6×10−3h70M⊙ yr−1 Mpc−3. Moreover, these numbers are
likely to be lower limits: if the discrepancy seen in Figure 13 is
due to internal extinction, then the true SFR density is probably ∼3.5
times higher.

The numbers above indicate that at z=3.1, the star-formation rate
density associated with Lyα emitters is comparable to that found
for Lyman-break galaxies. Before correcting for extinction, our number for
the LAE star-formation rate density is 8.6×10−3h70M⊙ yr−1 Mpc−3. For comparison, the LBG star-formation
rate density at z=3.1 (before extinction) is
∼0.01h70M⊙ yr−1 Mpc−3(Madau et al., 1998; Steidel et al., 1999). It is true that internal extinction within Lyman-break
galaxies is typically larger than it is in our LAEs,
E(B−V)∼0.15(Steidel et al., 1999). However, according to the
Calzetti (2001) extinction law, the effect of dust on the emission line
flux of a galaxy is much greater than that on the stellar
continuum. Consequently, our dust corrected SFR density for LAEs,
∼0.03h70M⊙ yr−1 Mpc−3, is ∼75% of the
LBG value. Of course, given the extrapolations and corrections required
to make this comparison, this number is highly uncertain.

The space density of z=3.1 Lyα emitters shown in Figure 11
translates into a surface density of 4.6±0.4 arcmin−2 per unit
redshift interval above our completeness limit. This number is similar to
that derived by Thommes & Meisenheimer (2005), under the assumption that the LAE phenomenon
is associated with the creation of elliptical galaxies and spiral bulges.
It is also consistent with the semi-analytical hierarchical structure
calculations of Le Delliou et al. (2005), though the latter predict a slightly
larger number of z∼3 LAEs than found in this paper. This difference is
not significant, since the Le Delliou et al. (2005) models have been adjusted to
match the previous small-volume Lyα surveys of Kudritzki et al. (2000) and
Cowie & Hu (1998). A ∼30% re-scaling of the escape fraction of Lyα
photons solves the discrepancy, and maintains the match between the
predictions and the faint-end slope of the galaxy luminosity function.

More notable is the excellent agreement between the Le Delliou et al. (2006)
simulations and the observed distribution of Lyα equivalent widths
(Figure 9). Both are very well-fit via an exponential with a
large (∼75 Å) scale length. Moreover, the models also predict that the
scale length observed for a magnitude-limited sample of galaxies (such as
that produced by the Lyman-break technique) will be much smaller than that
found via an emission-line survey. This is consistent with the LBG results
found by Shapley et al. (2003).

Nevertheless, we should emphasize that the LAEs detected in this survey are
probably not primordial galaxies in their initial stages of star-formation.
Very few of the objects have the extremely high equivalent widths calculated
for stellar populations with top-heavy initial mass functions. More
importantly, the scatter in the galaxies’ m1060−m1570 colors,
along with the offset between the Lyα and UV continuum star-formation
rates, suggests that these objects possess a non-negligible amount of dust.
The existence of this dust argues against the Pop III interpretation of
z∼3 Lyα emitters (Jimenez & Haiman, 2006).

The extremely strong line emission associated with LAEs makes
these objects especially suitable for probing the evolution of galaxies and
structure in the distant universe. The space density of z=3.1 emitters
shown in Figure 11 translates into a surface density of
4.6±0.4 arcmin−2 per unit redshift interval above our
completeness limit. This, coupled with our measured luminosity function,
implies that in the absence of evolution, there are ∼12 LAEs
arcmin−2 brighter than 1.5×10−17 ergs cm−2 s−1
in the redshift range 2<z<4. Wide field integral field units,
such as those being designed for ESO (Henault et al., 2004) and the Hobby-Eberly
Telescope (Hill et al., 2006) will therefore be able to find large numbers of
Lyα emitters in a single pointing. Moreover, because the faint-end of
the luminosity function is steep (α∼−1.5), the density of LAEs
goes linearly with survey depth. Dropping the flux limit by a factor of
two (to 7.5×10−18 ergs cm−2 s−1)
will roughly double the number of LAEs in the sample.

With an integral-field spectrograph, it is also possible to increase the
sample of high-redshift galaxies by identifying objects with equivalent
widths lower than our detection threshold of 80 Å (∼20 Å in the
LAE rest frame). However, the gain in doing so is likely to be
small: according to Figure 9, Lyα rest-frame equivalent
widths e-fold with a scale length of ∼75 Å. If this law
extrapolates to weaker-lined systems, as suggested by the models of
Le Delliou et al. (2006), then most Lyα emitters are already
being detected, and pushing the observations to lower equivalent widths
will only increase the number counts by ∼20%. Furthermore, as the data
of Hogg et al. (1998) demonstrate, contamination by foreground [O II] objects
increases rapidly once the equivalent width cutoff drops below ∼50 Å in the observers frame (or ∼12 Å in the rest frame of Lyα).
Unless one can accept a large increase in the fraction of contaminants,
surveys for high-redshift galaxies need to either stay above this
threshold, or extend to the near-IR (to detect Hβ and [O III]
λ5007 in the interlopers).

We would like to thank Kathy Durrell for her assistance in reducing the
data, Sean Points and Tim Abbott for their work deriving
the transmission curve of the CTIO [O III] interference filter, and
Cedric Lacey for providing the Le Delliou et al. (2006) models.
This work was supported by NSF grants 00-71238 and 01-37927 and
HST AR10324.01A. EG and JF acknowledge the support of NSF Astronomy &
Astrophysics Postdoctoral Fellowships, NSF grants 02-01667 and 03-02030.
Facilities:Blanco (Mosaic)

Figure 1: The bandpass of our narrow-band λ5000 filter, along with
those of the B and V filters, which are used to define the
continuum. A spectrum of a typical z=3.1 Lyα galaxy is
overlaid for comparison. Our narrow-band filter isolates the emission
line of Lyα sources with 3.09≲z≲3.13.

Figure 2: Excess emission in the narrow-band λ5000 filter over the continuum
for objects in our survey field. The abscissa gives the instrumental λ5000 magnitude, while the ordinate shows the difference between the sources’
narrow-band and B+V continuum AB magnitudes. Our narrow-band completeness
limit of 1.5×10−17 ergs cm−2 s−1 is represented by a
vertical line; our equivalent width limit of 90 Å is shown via the
horizontal line. The curve shows the expected 1σ errors in the
photometry. Candidate emission line galaxies are denoted as blue circles;
the green dots indicate LAE candidates found by our detection algorithms, but
rejected upon visual inspection.

Figure 3: Narrow-band λ5000, B+V, and difference images for three
candidate emission-line galaxies. Each frame is 10\arcsec on a side,
with north up and east to the left. The objects span a range of
brightness from logF5000=−15.60 at the top to logF5000=−16.74 at the bottom.

Figure 4: The left-hand panel shows the transmission curve for our
narrow-band λ5000 filter at the outside ambient temperature
and in the converging f/3.2 beam of the 4-m telescope. Note that the
bandpass is nearly Gaussian in shape. The arrow shows the transmission
value used to translate AB magnitude into monochromatic flux
(see text). The center panel uses the transmission function to illustrate
how our survey volume changes with emission-line sensitivity. The
right-hand panel translates the transmission function into the photometric
convolution kernel that is described in the text.

Figure 5: The sky coordinates of the 160 candidate z=3.1 LAEs
brighter than our completeness limit plotted over our narrow-band
5000 Å image. The size of each circle is proportional
to Lyα luminosity, with the largest circle representing
1.25×1043h70−2 ergs s−1. The green regions show
areas of the chip near bright stars that were excluded from the analysis;
the large rectangle is the GOODS field.

Figure 6: The B−R (rest frame m1060−m1570) color-magnitude diagram for
LAEs. The solid circles represent galaxies which have been spectroscopically
confirmed as Lyα emitters (Lira et al., 2007); the cross indicates the lone
AGN. The long-dashed line at R=24 represents the typical magnitude
limit of LBG spectroscopic surveys; the short-dashed line at R=25.5 gives
the photometric limit of most LBG observations. Note that the median
color of our LAEs is quite blue; this is consistent with models
for galaxies with recent star formation. Note also
the large range of colors displayed in the figure. This scatter is
greater than that expected from the photometric errors, and suggests that
the LAE population is not homogeneous.

Figure 7: The U−V versus V−R colors of our z=3.1 LAEs. The solid circles
show spectroscopically confirmed LAEs, the open circles represent
sources observed with insufficient signal-to-noise for classification,
and the crosses are objects with no spectroscopy. The dots are the
entire 84,410 object catalog. The polygon is the LBG
selection region; the sold curve is the track of an LBG template
spectrum. This track falls inside the selection region in the redshift
range 2.8<z<3.4(Shapley et al., 2003). Although most LAEs have LBG-like
colors, their R>25.5 magnitudes exclude them from the “spectroscopic”
samples studied by Steidel et al. (1996a, b, 2003).
The contribution of each LAE’s emission line to its
V-band flux has been subtracted to yield Vcorr.

Figure 8: The RAB (rest frame 1570 Å) luminosity function of our z=3.1
Lyα emitters (solid circles), compared to the rest-frame 1700 Å luminosity function of z=3.04 Lyman-break galaxies (open circles) from
(Steidel et al., 1999).
The flattening of our luminosity function at R>26.5 is due to selection:
at these magnitudes, only the strongest line emitters make it into
our sample. In the magnitude range R<25.5, z=3.1 Lyα
emitters are ∼3 times rarer than Lyman-break galaxies.

Figure 9: The top panel shows the observed distribution of equivalent widths for all the
Lyα emission-line galaxies in our sample. The dotted line shows the
apparent best-fit exponential for the distribution; the solid curve shows the
exponential after correcting for the effects of photometric error and our
filter’s non-square transmission curve. The lower two panels divide the
sample in half, and demonstrate that the exponential law does not change
much with galaxy luminosity. The vertical dashed line shows the maximum
equivalent width expected for populations with normal initial mass functions.

Figure 10: The number density of z=3.1 Lyα galaxies with observers’ frame
equivalent widths greater than 90 Å binned into 0.2 mag intervals. The
points give the density of objects under the assumption that our filter’s
FWHM defines the survey volume; the open circles represent data beyond
our completeness limit. The solid curve shows our input best-fit
Schechter (1976) luminosity function, while the dashed line illustrates
the shape and normalization of this function after correcting for the effects
of photometric error and our filter’s non-square transmission curve.

Figure 11: Maximum likelihood confidence contours for our Schechter (1976) function
fit to the observed distribution of Lyα fluxes. The three parameters
in the analysis are the faint-end slope (α), the bright-end cutoff
(logL∗) and the space density of galaxies with observed monochromatic
fluxes greater than 1.5×10−17 ergs cm−2 s−1,
i.e., LLyα>1.3×1042h70−2 ergs s−1.
The contours of probability are drawn at 1σ intervals.

Figure 12: The cumulative Lyα luminosity function inferred from our
survey of Lyα emitters with rest-frame equivalent widths
greater than 22 Å. The solid blue line shows our best fit
Schechter (1976) function (α=−1.49), the green line is the
α=−1.5 luminosity function found by Malhotra & Rhoads (2004) for LAEs
at z=5.7, and the red line is the Schechter fit for z=5.7
emitters found by Shimasaku et al. (2006). The dashed line is Model A
by Le Delliou et al. (2006). For purposes of this figure, our data have been
artificially normalized to match our best-fit function. The large
difference between the Malhotra & Rhoads (2004) and Shimasaku et al. (2006) fits makes it
impossible to study the evolution of the LAE population at this time.

Figure 13: A comparison of the star formation rates derived from Lyα emission
(under Case B recombination) and the UV continuum at 1570 Å. The solid
dots represent spectroscopically confirmed objects (Lira et al., 2007). The
diagonal dashed line shows where the two measurements are equal, while the
solid line illustrates where the UV continuum star-formation rate is three
times the Lyα rate. Our flux limit is shown via the vertical dashed
line; the approximate location of our equivalent width threshold is
shown via the dotted line (see text). Note that, although the two
indicators are correlated, the Lyα-inferred rates are ∼3
times less than those derived from the UV continuum.

Figure 14: Estimates of the internal extinction within our Lyα emitters,
formed using the assumption that the galaxies’ ionized gas is attenuated
more than its stars (Calzetti, 2001). The solid dots represent
spectroscopically confirmed Lyα emitters; the dashed line shows
the monochromatic flux limit of our survey. Note that very little
internal extinction is needed to bring the UV and Lyα star-formation
rates into agreement: even in the bright (R>24.5) galaxies, the internal
extinction is never more than E(B−V)stars∼0.1.

Figure 15: The results of our maximum likelihood analysis for the contribution
of Lyα emitters to the star formation rate density of the universe.
The abscissa is the star formation rate density derived from the observed
luminosity of the Lyα emission line; the ordinate is the relative
probability of a solution. The dashed line shows the observed
star formation rate density associated with galaxies above our completeness
limit, i.e., without any extrapolation of the galaxy luminosity function.
No correction for internal extinction has been applied. The figure implies
that the amount of star formation taking place in galaxies with
strong Lyα emission is comparable to that in Lyman-break galaxies.